Method and system for object recognition using fractal maps

ABSTRACT

A method for recognizing an object in an image is disclosed wherein a fractal map of the image is generated by estimating the fractal dimension of each pixel in the image. The fractal map may be segmented by thresholding and locations of candidate objects are determined. The pixel value of the image pixel corresponding to the same location where the candidate object is found in the fractal map may be compared to a threshold value. If the pixel value is greater than the threshold value, the candidate object is recognized as a valid object.

CROSS-REFERENCE TO RELATED APPLICATION

This is a continuation application of U.S. patent application Ser. No.12/028,934, filed Feb. 11, 2008, which is a continuation of U.S. patentapplication Ser. No. 11/745,245, filed May 7, 2007, which is acontinuation application of U.S. patent application Ser. No. 11/259,432,filed Oct. 26, 2005, now U.S. Pat. No. 7,215,829 and U.S. patentapplication Ser. No. 10/368,049, filed Feb. 14, 2003, now U.S. Pat. No.6,993,187, the entire contents of which are incorporated herein byreference in their entirety.

FIELD OF THE INVENTION

The present invention relates to digital image processing. Morespecifically, the invention relates to methods for object recognition inan image using both the image and the fractal map of the image.

BACKGROUND OF THE INVENTION

A human can view an image and effortlessly distinguish a face from thebackground even when the image is of poor quality. Providing this samecapability to a computer requires more effort. Distinguishing objects inan image is called pattern recognition and comprises three major steps:isolation; extraction; and classification. The first step, isolation,segments each object in the image. Extraction measures a set offeatures, such as size or color that characterizes each object. Lastly,classification assigns each object to a class based on the set ofmeasured features of the object. Castleman, Digital Image Processing,pp. 447-546, Prentice-Hall, (1996) describes each of the steps and isherein incorporated by reference.

Thresholding is one method of segmenting an image and has the advantageof being computationally simple. The pixel value of each pixel in theimage is compared against a threshold value and assigned a new pixelvalue depending on whether the original pixel value is greater than orless than the threshold value. Thresholding works well when the object,or target, of interest has a substantially uniform gray level that issignificantly different from the gray level of the background.

A common problem in automated image processing systems is that thethreshold value required to properly segment the image depends on thequality of the images being processed. Adaptive threshold systems adjustthe threshold value according to the image characteristics, but requiremore computational resources that may make the application costprohibitive. Alternatively, if the samples are fairly uniform, such asPC boards, and the lighting conditions during image capture are tightlycontrolled, the threshold value may be set once at the beginning of theautomated inspection process.

FIG. 1 is a schematic of an automated scanning optical microscopysystem. The automated scanning optical microscopy system 100 includes anoptical microscope modified to automatically capture and save images ofa sample 105 placed on a sample holder 107 such as, for example, aslide, which in turn is supported by a stage 110. The optical componentsinclude an illumination source 120, objective lens 124, and camera 128.Housing 130 supports the optical components. The design and selection ofthe optical components and housing are known to one of skill in theoptical art and do not require further description.

The automated system 100 includes a controller that enables the stage110 supporting the slide 107 to move a portion of the sample 105 intothe focal plane of the objective lens and to translate the stage withinthe focal plane of the objective lens to allow different portions of thesample to be viewed and captured. The camera 128 captures an image ofthe sample and sends the image signal to an image processor for furtherprocessing and/or storage. In the example, shown in FIG. 1, the imageprocessor and controller are both housed in a single PC 104 althoughother variations may be used. The mechanical design of the stage 110 isknown to one of skill in the mechanical arts and does not requirefurther description.

The controller may also control a sample handling subsystem 160 thatautomatically transfers a slide 109 between the stage 110 and a storageunit 162. The prepared sample slides are loaded into the storage unit162 and the storage unit 162 is loaded on the sample handling subsystem160. The loading of the slides into the storage unit or the loading ofthe storage unit into the handling subsystem may be done manually by anoperator or may be automated. After the handling subsystem is loaded,the operator may enter information describing or identifying the samplesinto the processor. The operator may also enter or select parametersthat govern how the scanning microscopy system will operate during theautomated run. For example, the operator may choose to process all ofthe loaded sample slides in one continuous run or choose to terminatethe run after a selected number of slides have been processed. As afurther example, the operator may view one or more images captured fromthe samples and set threshold values such as the ones described below.After the run parameters are entered, the operator starts the run andthe processor takes control of the system until the run is completed orterminated by the controller.

The image captured by the camera 128 may be preprocessed before beingstored or sent to the image processor. The hardware and basic softwarecomponents for the capture, storage, retrieval, display, andmanipulation of the image are known to one of skill in the art and arenot further discussed. The image processor may correct for cameraartifacts, enhance particular objects of the image to simplify theobject recognition process, or adjust or compensate for the lightingconditions used to capture the image.

In many situations, however, the properties of the sample itself produceimages where the pixel values (gray levels) of the background do notdiffer significantly from the pixel values of the target. For example,epifluorescence microscopy of biological samples usually produces lowlight signal images because of the low signal strength of thefluorophore used to tag the biological samples. Under low lightconditions, the average pixel value of the image is close to zero. Asimilar situation occurs under low contrast conditions where thedifference between the average pixel value of the target and the averagepixel value of the background is close to zero. In both conditions,closeness is relative to the maximum pixel value. For example, if thepixel depth is eight bits, the maximum pixel value is 255 and a pixeldifference of 16 may be considered close. Similarly if the pixel depthis 16 bits, the maximum pixel value is 65,535 and a pixel difference of512 may be considered close. If the threshold is set to the averagepixel value when the average value is close to zero, the segmentationwill be susceptible to false positives due to background noise.

Therefore, there remains a need for a method of image segmentation thatmay be used in automated image processing systems that is capable ofhandling low light low contrast images.

SUMMARY

One embodiment of the present invention is directed to a method ofrecognizing an object in a digital image, the method comprising:generating a fractal map of the image; isolating the object bysegmenting the fractal map; locating the object on the fractal map; andconfirming the object based on a pixel value of a pixel at acorresponding location in the digital image. In some embodiments, themethod of segmenting the image further includes applying a threshold tothe fractal map, the threshold representing a fractal dimension. In someembodiments, generating the fractal map further includes: forming aplurality of boundary images from the image, each of the plurality ofboundary images characterized by a scale; estimating the fractaldimension of at least one pixel of the image from the plurality ofboundary images; and setting a pixel in the fractal map corresponding tothe location of the at least one pixel of the image a value equal to theestimated fractal dimension of the at least one pixel. In someembodiments, forming the boundary image further includes: eroding theimage by an L×L structuring element to form an eroded image: dilatingthe image by an L×L structuring element to form a dilated image; andforming the boundary image by subtracting the eroded image from thedilated image, the scale of the boundary image defined by L. In someembodiments, generating the fractal map includes estimating a fractaldimension for at least one pixel of the image, the fractal dimension ofthe pixel given by

$d_{p} = \frac{\begin{matrix}{\log \left( \frac{N_{2}}{N_{1}} \right)} \\{\log \left( \frac{N_{2}}{N_{1}} \right)}\end{matrix}}{\log \left( \frac{L_{2}}{L_{1}} \right)}$

where d_(p), is the fractal dimension of the at least one pixel of theimage. N₂ is the sum of the pixel values in an L₂×L₂ structuringelement. N, is the sum of the pixel values in an L₁×L₁ structuringelement, and L₂ and L₁ are the sizes (in pixels) of the respectivestructuring elements.

Another embodiment of the present invention is directed to a system forautomatically recognizing an object in a digital image, the systemcomprising: an image capture sensor for capturing the image, the imagecomprising at least one pixel, the pixel characterized by a location ofthe pixel within the image and a pixel value; means for generating afractal map of the image; means for segmenting the fractal map; meansfor locating the object on the fractal map; and means for recognizingthe object based on a pixel value at a corresponding location in thedigital image. In some embodiments, the means for generating the fractalmap further comprises means for estimating the fractal dimension of theat least one pixel of the image and assigning the estimated fractaldimension to a pixel value of a pixel in the fractal map correspondingto the location of the at least one pixel of the image. In someembodiments, the means for estimating the fractal dimension furtherincludes: means for applying a first structuring element to the at leastone pixel of the image, the first structuring element characterized by afirst scale length; and means for applying a second structuring elementto the at least one pixel of the image, the second structuring elementcharacterized by a second scale length, wherein the second scale lengthis greater than the first scale length.

BRIEF DESCRIPTION OF THE DRAWINGS

The invention will be described by reference to the preferred andalternative embodiments thereof in conjunction with the drawings inwhich:

FIG. 1 is a schematic diagram of an automated scanning opticalmicroscopy system;

FIG. 2 is a flowchart of an embodiment of the present invention;

FIG. 3 is a flowchart illustrating the generation of a boundary image inan embodiment of the present invention;

FIG. 4 a is a diagram illustrating an L=3 structuring element used inone embodiment of the present invention;

FIG. 4 b is a diagram illustrating an L=3 structuring element used inanother embodiment of the present invention;

FIG. 5 is an illustrative example showing two images and their fractalmaps generated by the embodiment shown in FIG. 2.

FIG. 6 is a flowchart of another embodiment of the present invention.

FIG. 7 is a flowchart of the confirmation method of the embodiment shownin FIG. 6.

DETAILED DESCRIPTION OF THE PREFERRED AND ALTERNATIVE EMBODIMENTS

Low light/low contrast images may be adjusted by mapping the pixelvalues to a transformed set of pixel values. For the purposes ofillustration, suppose an image having a depth of eight bits has pixelvalues between 0 and 31. The image is a low light image because thegreatest pixel value of the image, 31, is much less than the maximumpossible pixel value of 255. Histogram equalization maps the pixelvalues of the original image to pixel values that span the entire pixeldepth. In this example, pixels having a pixel value of 31 are, given anequalized pixel value of 255, pixels having a pixel value of 16 aregiven an equalized pixel value of 128, etc. Histogram equalization is alinear mapping, but contrast may be further enhanced by a non-lineartransformation such as a power law. One such non-linear transformationis the gamma correction that calculates the corrected pixel value basedon the original pixel value raised to a constant, γ.

Both histogram equalization and gamma correction are pointtransformations in that the transformed pixel value does not depend onthe pixel values of the neighboring pixels. Filtering operations suchas, for example smoothing calculate the new pixel value based on thepixel values in the neighborhood of the structuring element. Thefiltering operation is completed in one sweep through all the pixels inthe image using the same sized structuring element or filter kernel. Thesize of the structuring element determines the extent of sampling of theneighboring pixels. These operations are described in Castleman and donot require further discussion.

In one embodiment of the present invention, a fractal map is generatedfor each image that allows thresholding for low light/low contrastimages without the need for histogram equalization or gamma corrections.Unlike histogram equalization or gamma corrections, the fractaltransformation is not a point operation and uses the pixel values ofneighboring pixels to calculate the transformed pixel value. Unlikefiltering operations, the fractal transformation samples at least twoneighborhoods where each neighborhood is characterized by a differentsize, or scale.

The fractal map is generated by assigning to each pixel in the image apixel value that represents the fractal dimension of the pixel. Adescription of fractals is given in Mandelbrot, The Fractal Geometry ofNature. W. H. Freeman, San Francisco (1982) and is herein incorporatedby reference. Mandelbrot uses the fractal dimension to describeself-similar objects such as the Koch curve or fracture surfaces inmaterials.

The fractal dimension is the exponent in a poser law function relating ameasurable quantity to a length raised to the exponent. i.e.,

N=ρL^(d)  (1)

where N is a countable quantity such as the number of pixels defining anedge, p is a density, L is a scale length, and d is the fractaldimension. Although d may be an integer, in most cases d is anon-integer.

Mandelbrot describes one method of determining the fractal dimension ofan object by counting the number of covering spheres required to coverthe object as a function of the covering sphere size. The fractaldimension of the object is the slope of the number of covering spheresversus covering sphere size when plotted on log axes. If only two spheresizes are used, the fractal dimension may be estimated by the equation:

$\begin{matrix}{d = \frac{\log \left( \frac{N_{2}}{N_{1}} \right)}{\log \left( \frac{L_{2}}{L_{1}} \right)}} & (2)\end{matrix}$

where N₂ is the number of covering spheres of size L₂ required to coverthe object and N₁ is the number of covering spheres of size L₁ requiredto cover the object.

The fractal dimension, as described by Mandelbrot, is a single numberthat characterizes the whole object and is therefore global in the sensethat it represents the whole object. In a similar fashion, the fractaldimension has been used to characterize fracture surfaces as describedin Russ, Handbook of Image Processing 4th ed., pp. 261-263) 694-696, CRCPress, 2002, herein incorporated by reference. In both cases the fractaldimension is associated with the whole object and is determined once forthe object. The fractal dimension may be interpreted as representing ameasure of the shape and degree of self-similarity of the object.Assuming this interpretation is correct, then each portion of the objectshould also have the same fractal dimension as long as the size of theportion lies within the self-similar range of the object. Therefore, asingle determination of the fractal dimension of the object should besufficient to characterize the object.

The inventor, however, has discovered that when each pixel of an imageis assigned a fractal dimension using an equation of the same form asequation (2) but where N₁ and N₂ are the sums of pixel values instead ofthe number of pixels, the resulting gray scale fractal map of the imagemay be segmented simply and accurately even for low light/low contrastimages. As used hereinafter, the term fractal dimension refers to thequantity, d, estimated using the equation (2) where N₁ and N₂ are thesums of pixel values instead of the number of pixels

FIG. 2 is a flow diagram of one embodiment of the present invention. Animage, l₀, is read in step 205. In step 210, a first boundary image,l_(B1), is generated from l₀ and stored. A second boundary image,l_(B2), is generated from l_(O) and stored in step 215.

FIG. 3 is a flow diagram illustrating the generation of each boundaryimage, Is. An erosion image, E^(L), is generated from the capturedimage, l₀, and stored in step 310. A dilation image, D^(L), is generatedfrom lo and stored in step 320. In step 330, the boundary image, l_(B),is generated by subtracting the erosion image from the dilation image,i.e., l_(B)=D^(L)−E^(L). The superscript, L, in E^(L) and D^(L) bothrefer to the size, or scale, of the structuring element used to performthe erosion or dilation, respectively.

The structuring element may be represented by an L×L matrix comprised ofones and zeros. The structuring element is characterized by an originpixel and a neighborhood. The neighborhood comprises all the matrixelements that are set to one and is contained within the L×L matrix. Animage is generated by calculating a pixel value for the pixel at theorigin of the structuring element based on the pixel values of thepixels in the neighborhood of the structuring element. In the case oferosion, the pixel value of the origin pixel is set to the minimum ofthe pixel values in the neighborhood. Dilation, in contrast, sets thepixel value to the maximum of the pixel values in the neighborhood. Inone embodiment, the neighborhood is coextensive with the structuringelement where the L×L matrix comprised of all ones as shown in FIG. 4 afor an L=3 structuring element. In another embodiment, the neighborhoodis less than the structuring element in that the L×L matrix includes atleast one zero. In another embodiment, the neighborhood is a “cross” or“plus” centered on the origin of the structuring element, as shown inFIG. 4 b for an L=3 structuring element.

Referring to FIG. 2, step 215 generates a second boundary image, l_(B2)at a different scale, L₂, using a different size structuring elementthan the structuring element used to generate l_(B1). The selection ofthe scale for both boundary images may depend on the size of the objectof interest, the computational limitations of the processor, and othersuch factors as is apparent to one of skill in the art. In oneembodiment. L₁ and L₂ are selected to maximize the difference between L₁and L₂ under constraints such as those identified above. In oneembodiment, L₁ may be chosen from the group consisting of 1, 2, 3, 4, 5,and greater than 5. In a preferred embodiment, the scale of l_(B1) isset to L₁=3. L₂ is selected such that L₂ is greater than L₁, or, stateddifferently, the ratio, R=L₂/L₁>1. In one embodiment. R is in the rangeselected from a group consisting of 1-16, 16-64, 64-128, and greaterthan 128. In a preferred embodiment, R=85.

The fractal dimension, d_(p), for each pixel in l₀ is estimated from theboundary images l_(B1) and l_(B2) in step 220. The fractal dimension foreach pixel may be estimated by the equation (3):

$\begin{matrix}{d_{p} = \frac{\log \left( \frac{N_{2}}{N_{1}} \right)}{\log \left( \frac{L_{2}}{L_{1}} \right)}} & (3)\end{matrix}$

where N₂ represents the sum of the pixel values in the neighborhood ofthe structuring element centered on the pixel in l_(B2) and N₁represents the sum of the pixel values in the neighborhood of thestructuring element centered on the pixel in l_(B1).

The image generated by the set of d_(p)s s is called the fractal map orfractal image. Unlike l₀ where the pixel values represent a lightintensity for the pixel location in the image, the pixel values in thefractal map represent the fractal dimension for that pixel location inthe image.

The form of equation (3) clearly shows that the fractal dimension isestimated by taking ratios of pixel values and therefore should providea more robust method than histogram equalization or gamma correction fordistinguishing objects in low light or low contrast conditions.Furthermore, it is believed that the use of sums in N₁ and N₂ reducesthe statistical variations that may be expected in low light conditions.

The image, l₀, is segmented in step 230. In a preferred embodiment, thesegmentation of l₀ is accomplished by thresholding the fractal map of l₀and using the one-to-one correspondence of a fractal map pixel to theimage pixel to segment the image. The threshold value may be set once byan operator prior to an automated run of a batch of samples, or may bedynamically adjusted during the automated run via the techniquesdescribed in, for example, Russ. The threshold value may be determinedusing a calibrated sample or, more preferably by using a few samplesfrom the batch.

FIG. 5 shows enhanced images and their respective fractal maps of asample and illustrates the ability of the fractal map to distinguish thetarget of interest. Images 510 and 530 are 256×256×8 images of a malefetal cell in a maternal blood sample. The sample was tagged with probesfor the X and Y-chromosomes. Image 510 is obtained using a filter thatallows the emission light from the X chromosome probe to pass through tothe camera. Image 530 is obtained using a filter that allows theemission light from the Y chromosome probe to pass through to thecamera.

Images 510 and 530 have been histogram equalized and gamma corrected inan attempt to visually enhance the quality of the images and allow theviewer to see the relevant objects of the images 510 and 530. In spiteof these enhancements, the images still do not clearly display theobjects of interest. The maximum pixel value for each image 510 and 530are indicated in FIG. 5. The Xprobe image 510 has a maximum pixel valueof 74. The X-probe image 510 also shows a second object, an artifact,having a pixel value of about 36. The maximum pixel value of the Y-probeimage 530 is 42. Both images 510 and 530 are low light images becausethe maximum pixel value of each image is much less than the gray scalerange for the images, which, in this case, is 2⁸ or 255.

The difficulty in segmenting both images 510 and 530 using a single grayscale threshold value is clear. If the gray scale threshold value is setto, for example, 60 in order to separate the X-probe signal from theartifact signal in the Xprobe image, the Y-probe signal will not bedetected because its pixel value is less than the gray scale thresholdvalue of 60. If, on the other hand, the gray scale threshold value isset to a value around 30 in order to pick out the Y-probe signal, boththe X-probe signal and the artifact will be segmented in the X-probeimage. In order to select the Y-probe signal and reject the artifact,the threshold must be set to a very narrow range between 36 and 42.Setting the threshold to such a narrow range makes the segmentationprocess susceptible to many errors if the image quality is changedslightly. Unless the gray scale threshold is adjusted for each image,segmentation errors such as the ones described above are likely tooccur. Adjusting the threshold value for each image, either manually orautomatically, will, however, reduce the throughput rate of the samplingsystem.

The X-probe fractal map 515 and the Y-probe fractal map 535 shown inFIG. 5 are generated from their respective images using structuringelements of size 3 and 255. The images were not histogram equalized norgamma corrected prior to generating the fractal maps. The fractaldimensions of the pixels, d, corresponding to the corresponding pixelsin the gray scale image are shown in FIG. 5. The fractal dimension ofthe N-probe pixel is 2.41, the artifact has a fractal dimension of 2.21,and the fractal dimension of the Y-probe pixel is 2.41. In comparingfractal maps 515 and 535, it appears that the fractal transformationtends to equalize the dominant signal across each image and separate thedominant signal from a subordinate signal within each image. In thisexample, a single fractal threshold may be used to segment both theN-probe and Y-probe signals from the rest of their respective fractalmaps. The apparent ability of the fractal transformation to assign thebrightest or dominant signal roughly the same value regardless of imagequality reduces the need to dynamically adjust threshold values for eachimage or to generate consistent, high quality images for an entiresample batch.

In another embodiment of the present invention, an automated method foridentifying male fetal cells in maternal blood is now described. Asample of maternal blood is prepared by staining the nuclear materialwith a dye such as DAPI following procedures known to one of skill inthe art. The sample is also tagged with FISH probes targeted to the Xand Y-chromosomes. High magnification (about 100×) images of a portionof the prepared sample are captured by a monochrome camera after passingthrough a filter that passes one of the probe signals through to thecamera. The images captured through the X-probe filter are hereinafterreferred to as the N-images. Similarly, the images captured through theY-probe filter are hereinafter referred to as the Y-images. For eachportion of the sample, n images, each taken at a different focaldistance, are captured and stored. The number, n, is selected to ensurethat the probe lies in the focal plane of one of the n images anddepends on the depth of field of the objective used to capture the imageand the expected thickness of the sample. As an illustrative example, ifthe objective has a depth of field of about 0.8 pm and the estimatedsample thickness is about 7 μm, a set, or stack of n=9 images should besufficient to ensure that the probe lies in the plane of at least one ofthe images in the stack.

FIG. 6 is a flowchart illustrating the method of identifying male fetalcells in maternal blood. Although the description below is limited to asingle image stack, it is understood that the flowchart in FIG. 6 isfollowed for both the X-image stack and the Y-image stack.

A binary mask isolating the nucleus from the rest of the image iscreated in step 610. The mask is created by thresholding the DAPI signalfollowed by a closing operation. The threshold value is preferably setto between 1.2-2.0 times the background and most preferably set tobetween 1.4-1.6 times the background.

A composite image, referred to as the Max image, is generated in step620. The pixel value for each pixel in the Max image is the maximum ofthe corresponding pixel values among the n images in the image stack,i.e.,

Max(x,y)=MAX{X1(x,y),X2(x,y), . . . Xn(x,y)}  (4)

where Max(x, y) is the pixel value at the location (x, y) in the Maximage, Xi(x, y) is the pixel value at the location (x, y) in the i-thimage of the image stack, and MAX{argument list} is the maximum functionreturning the largest value in the argument list.

The objects external to the nucleus are eliminate in step 630 byperforming an AND operation with the binary mask created in step 610 andthe Max image generated in step 620.

A fractal map of the image created in step 630 is generated in step 640following the procedure described above. In an alternative embodiment,the fractal map is generated directly from the Max image. The fractaldimension for a pixel is estimated by centering a L₁×L₁, structuringelement on the pixel and summing the pixel values of the pixels withinthe structuring element to form a first sum, N₁. A second structuringelement of size L₂×L₂, where L₂>L₁, is center on the pixel and a secondsum, N₂, of the pixel values of the pixels within the second structuringelement is calculated. The fractal dimension of the pixel is estimatedusing the equation

$\begin{matrix}{d_{p} = \frac{\log \left( \frac{N_{2}}{N_{1}} \right)}{\log \left( \frac{L_{2}}{L_{1}} \right)}} & (5)\end{matrix}$

where d_(p), is the fractal dimension of the pixel in the Max image, N₂is the sum of the pixel values in the L₂×L₂ structuring element, N₁ isthe sum of the pixel values in the L₁×L₁ structuring element, and L₂ andL₁ are the sizes (in pixels) of the respective structuring elements.

In one embodiment, L₁ may be chosen from the group consisting of 1, 2,3, 4, 5, and greater than 5. In a preferred embodiment, L₁ is set toL₁=3. L₁ is selected such that L₂ is greater than L₁ or, stateddifferently, the ratio, R=L₂/L₁>1. In one embodiment, R is in the rangeselected from a group consisting of 1-16, 16-64, 64-128, and greaterthan 128. In a preferred embodiment, R=10.

The fractal map is segmented in step 650 by thresholding. In oneembodiment, a single threshold value may be used to segment the fractalmap. In a preferred embodiment, two segmented images are generated fromthe fractal map using a first threshold value to generate a firstsegmented fractal image and a second threshold value to generate asecond segmented fractal image. The threshold values are preferably setby an operator before the automated analysis of the sample run. Shethreshold value may be optionally adjusted automatically during theautomated run to compensate for sample-to-sample variations.

Objects in the segmented fractal images are shrunk to points in step660. The shrinking operation is repeated applied to the segmentedfractal image until the target objects are single pixels referred tohereinafter as dots. Alternatively, the shrinking operation may berepeated S times where S is a predetermined number that depends on theobject size and desired throughput rate.

The dots remaining after the shrinkage operation 660 should correspondto the probe signals in the Max image. As a check, the dots in thesegmented fractal image are compared to the corresponding location inthe Max image in step 670. If the dots represent true probe signals, thepixel value of the corresponding pixel in the Max image should be one ofthe largest pixel values in the Max image.

FIG. 7 is a flowchart illustrating the details of the confirmation checkof step 670. In FIG. 7, the Max image is corrected for background beforecomparison to the segmented fractal map. The background of the Max imageis estimated in step 710. In a preferred embodiment, a first minimumpixel value from a first set of pixels is compared to a second minimumpixel value from a second set of pixels and the greater of the first orsecond minimum pixel value is selected as the background, b. In apreferred embodiment, the first set of pixels forms a line across theMax image. Similarly, the second set of pixels forms a second lineacross the Max image. In a preferred embodiment, the first and secondlines intersect at or near the center of the Max image. In anotherembodiment, the first line is a vertical line through the center of theMax image and the second line is a horizontal line through the center ofthe Max image.

The background adjusted Max image, Mb, is generated in 720 by settingpixels in the Max image having a pixel value that is less than twice thebackground estimated in step 710 to zero as shown in equation 6:

$\begin{matrix}{{p_{b}\left( {x,y} \right)} = \left\{ \begin{matrix}{p\left( {x,y} \right)} & {{p\left( {x,y} \right)} > {2*b}} \\0 & {otherwise}\end{matrix} \right.} & (6)\end{matrix}$

where p_(b)(x−y) is the pixel value at location (x,y) in the Mb image,p(x,y) is the pixel value at location (x,y) in the Max image, and b isthe background.

A threshold for M_(b) is set in step 730. In a preferred embodiment, ahistogram is generated for M_(b). Starting at the bin containing thedarkest or lowest pixel value, one or more bins are examined for anon-zero value. A bin containing a zero value indicates that no pixelsin M_(b) have a pixel value represented by the bin. Conversely, a bincontaining a non-zero value indicates that there is at least one pixelin M_(b) having a pixel value represented by that bin. The bins aresequentially searched until the first non-zero value is found. The pixelvalue represented by the bin with the first non-zero value is added toan offset and the sum is set as the threshold, T.

The offset may be determined and set by an operator before a run. Theoffset will depend on the quality of the images in the run but may beeasily determined empirically by one of skill in the art. As anillustrative example, gray scale images 510, 530 of FIG. 5 are lowquality in that the maximum pixel value is less than 100. An offset inthe range of 5-20 may be appropriate for such images. In contrast, alarger offset value may be used for higher quality images.

In step 740, the objects (dots) identified in the fractal map arechecked to confirm the existence of corresponding objects in M_(b). Thepixel value of Max pixel corresponding to the location, (x_(f), y_(f)),where an object was detected in the fractal map is compared to thethreshold, T. i.e.,

p _(b)(x _(f) ,y _(f))>T  (7)

where p_(b)(x_(f), y_(f)) is the pixel value of the M_(b) pixel atlocation (x_(f), y_(f)) and x_(f) and y_(f) are the x and y coordinatesof the object detected in the fractal map.

If the Max pixel is not greater than the threshold, the object isconsidered to be a false signal and is not counted. If, on the otherhand, the Max pixel is greater than T; the object is recognized as atrue signal and is counted in step 745 by incrementing a count value.

In step 750, a check is made to verify that all detected objects in thefractal map have been compared to its corresponding Max image pixelvalue. If all objects have been compared, the process exits in step 760.If there are remaining objects, the process returns to step 740 usingthe location of the remaining object.

Count step 745 may store the count value for latter processing. In analternative embodiment, the count value may be compared to an expectedvalue and an error flag set if the count value exceeds the expectedvalue. As an illustrative example, if only one probe signal is expectedper nucleus, the expected value may be set to 1. As another illustrativeI example, if the probe signal represents the Y chromosome, the numberof expected signals is either 0 (for female) or 1 (for male). Theexpected value may be set to 1 because a count of 2 would represent agenetic abnormality or a false positive. In either situation, the imagecould be flagged for further analysis by an operator.

Having described at least illustrative embodiments of the invention,various modifications and improvements will readily occur to thoseskilled in the art and are intended to be within the scope of theinvention. Accordingly, the foregoing description is by way of exampleonly and is not intended as limiting. The invention is limited only asdefined in the following claims and the equivalents thereto.

1. An apparatus for discriminating objects in a digital imagecomprising: an automated scanning optical microscopy system; a digitalcamera attached to said automated scanning optical microscopy system andconfigured to capture said digital image of field of view of saidmicroscopy system; an image processor configured to receive said digitalimage from said digital camera and to perform the steps of:automatically assigning to each pixel in the digital image a pixel valuethat represents the fractal dimension of the pixel to generate a fractalmap; segmenting the fractal map into two or more fractal images; andshrinking objects in the segmented fractal images.